Aptitude - Probability - Discussion

Discussion :: Probability - General Questions (Q.No.4)

4. 

What is the probability of getting a sum 9 from two throws of a dice?

[A].
1
6
[B].
1
8
[C].
1
9
[D].
1
12

Answer: Option C

Explanation:

In two throws of a dice, n(S) = (6 x 6) = 36.

Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.

P(E) = n(E) = 4 = 1 .
n(S) 36 9


Malasrvizhi said: (Oct 31, 2010)  
How did get the sum element?

Rama said: (Feb 14, 2011)  
How to select n(e) = 4.

Vian said: (Feb 17, 2011)  
@rama.

That is because the event of finding the sum 9 is 4.

Azam said: (Apr 22, 2011)  
In two throws of a dice, n(S) = (6 x 6) = 36.

HOW IT DO
PLEASE EXPLAIN

Krish said: (May 16, 2011)  
How it could be n(s)= (6 x 6)

Srinivas said: (Jun 15, 2011)  
n(s)=36

n(a)=[36][45][63][54]

p(a)=4/36=1/9

Sreejith said: (Jun 17, 2011)  
@Azam

In both throughs, it can be any of 1,2,3...,6(6C1 ways of selection). So total number of outcomes = 6C1*6C1 = 36

More clearly, the elements of sample spaces are

{(1,1),(1,2),(1,3),....,(2,1),(2,2),.....(6,1),(6,2),....(6,6)}

Hope you got it.

Harikannan said: (Jun 30, 2011)  
How to find event that is (3, 4) (4, 5) (5, 4) (6, 3) please explain.

Syam said: (Jan 5, 2012)  
{ (3, 6) , (4, 5) , (5, 4) , (6, 3) } is a case only.

We can get (6, 3) , (5, 4) , (3, 6) , (4, 5) also.

So answer is 8/38 = 2/9.

Am I correct ?

Ankita said: (Feb 4, 2012)  
How do we know that we have to pick up 6 * 6?

Anurag said: (Mar 12, 2012)  
Ankita:.

Because 6c1 * 6c1 is 36.

Kanchi said: (Sep 18, 2012)  
s is a sample space i.e all possible outcomes
if two coins are tossed then s={HH,TT,HT,TH}
same in this qu. two dice -use then no of possible outcome
s={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)},
{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)}
..........
{(6,1),(6,2),(6,3),(6,4),(6,5),(6,5)}

n(s)=6+6+6+6+6+6=36
or
6*6=36

Frederick Mattson said: (Aug 6, 2013)  
1,1 2,1 3,1 4,1 5,1 6,1
1,2 2,2 3,2 4,2 5,2 6,2
1,3 2,3 3,3 4,3 5,3 6,3
1,4 2,4 3,4 4,4 5,4 6,4
1,5 2,5 3,5 4,5 5,5 6,5
1,6 2,6 3,6 4,6 5,6 6,6

P(sum 9) = {(6,3),(5,4),(4,5),(3,6)}.

= 4/36.

= 1/9.

Narottam said: (Oct 13, 2013)  
Is there any short method to choose number of event ?

Muhammad Rizwan said: (Oct 20, 2013)  
I have a little bit confusion. Question is "What is the probability of getting a sum 9 from two throws of a dice?". Here we talk about two throws means that a dice is thrown 2 times.

Further it means that a single dice is throw 2 times. So, we should take sample space of 6 because of a single dice.

In case of 36 the question should be "What is the probability of getting a sum 9 when two dice are thrown?". Or perhaps I am in mistake in understanding the question. Please clear this.

Dhaval said: (Nov 15, 2013)  
If I three throw of dices than what is answer?

Ranjith said: (Dec 21, 2013)  
I understood of this way I don't know this is right or wrong.

We want to getting some 36 = 36+9 = 45.
45+9 = 54.
54+9 = 63.

Nitinpatel said: (Jan 20, 2014)  
How do it?

In two throws of a dice, n(S) = (6 x 6) = 36.

Sus said: (Jul 30, 2014)  
Is there any short method to choose number of event ?

Purushotham said: (Aug 30, 2014)  
Is there any short method to choose number of event ?

Prajapati Divya H said: (Aug 31, 2014)  
How do it?
In throws of a dice, n(s) = (6*6) = 36.

Sree Tulasi said: (Sep 23, 2014)  
In that question they have asked for 2 dices, it means each dice is having 6 sides. So for 2 dices= 6*6=36. n(S)=36

Then we should find the possibility for sum of 9 so we can take (4,5),(3,6),(6,3),(5,4). These are 4 possibilities for sum of 9. n(E)=4.

After that Probability of E = n(E)/n(S) = 4/36 = 1/9.

Rama said: (Oct 5, 2014)  
How we got n(e) i.e, 4. Please friends somebody help me to find out the answer.

Lettisha L.S said: (Oct 19, 2014)  
@Rama.

So n(e)=4. It's because the possible combinations where you would get sum 9 when you throw the dice twice are 4.

Like in a dice there are 1-6 no.s right? So what no.s do you put together to get sum 9? (3,6), (4,5), (6,3) ,(5,4) .

But these combos aren't possible: (2,7), (1,8) because well they're not on a dice.

Hope THAT cleared it up for you! ^_^.

Nani said: (Feb 16, 2015)  
How can we get outcomes as 36? Please explain.

Ajax said: (Feb 19, 2015)  
Short method of find sum of two dice.

Sum - Time.

2 - 1.
3 - 2.
4 - 3.
5 - 4.
6 - 5.
7 - 6.
8 - 5.
9 - 4.
10 - 3.
11 - 2.
12 - 1.

Reena said: (Apr 16, 2015)  
Two of a dice n(S) = 6*6 because 1 dice = 1, 2, 3, 4, 5, 6.

1 dice = 1, 2, 3, 4, 5, 6.

= 1(6)*1(6) = 36.

Let E = Event of getting a sum = {(3, 6), (4, 5), (5, 4), (6, 3)}.

= (3+6) = 9.
= (4+5) = 9.
= (5+4) = 9.
= (6+3) = 9.

As a question,

P(E) = n(E)/n(S) = 4/36 = 1/9.

John said: (Aug 13, 2015)  
Do you need to do all thus working out?

Laxmipriya said: (Sep 22, 2015)  
Why to do multiplication like 6*6=36? Why we can't do addition?

Like 6+6 = 12. I can't understand when to do addition and when to do multiplication.

Amol Pawar said: (Oct 4, 2015)  
Dice has 6 faces, i.e (1, 2, 3, 4, 5, 6) in this addition of 9 occurs when (5+4 or 4+5) and (6+3 or 3+6) that means 4 ways.

In this way n(e) = 4 and n(s) = 6*6 =36.

P (e) = n(e)/n(s) = 4/36 = 1/9.

Deepthi said: (Mar 20, 2016)  
By throwing 2 dies, to get a sum of 9 there are also possibilities of getting (1,8) (2,7) (3,6) (4,5) (5,4) (6,3) (7,2) (8,1) we have 8 possibilities please explain this.

Naimulsamad said: (Jun 11, 2016)  
Look in a dice there are number 1, 2, 3, 4, 5, 6.

To form as a 9 we need 6 + 5 + 4 + 3 number. Such as 5 + 4 = 9, 6 + 3 = 9 but 1 + 8 or 2 + 7 is not possible because dice do not contain the number 7, 8.

So sum up the number 6 +5 + 4 + 3 = 18 (one dice). 18 * 2 = 36 (two dice).

Chethan said: (Jul 20, 2016)  
Why they took n(E)/n(S)? In some other problem, they took n(S)/n(E).

Umar said: (Oct 21, 2016)  
9 + 9 = 18,
=> 2/18 = 1/9.

B.Lokesh said: (Oct 31, 2016)  
One dice means 6 faces.
Two dice means 6 * 6 = 36 faces.
Either,
(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)
(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)
(3,1)(3,2)(3,3)(3,4)(3,5)(3,6)
(4,1)(4,2)(4,3)(4,4)(4,5)(4,6)
(5,1)(5,2)(5,3)(5,4)(5,5)(5,6)
(6,1)(6,2)(6,3)(6,4)(6,5)(6,6)
Total = 36 outcomes.
So question ask that,
Sum =9.
So,
3 + 6 = 9 (3,6)
6 + 3 = 9 (6,3)
4 + 5 = 9 (4,5)
5 + 4 = 9 (5,4)
4 out comes.
p = num of outcomes/total outcomes.
p = 4/36 = 1/9.

Hope you understand this.

Shankar said: (Nov 29, 2016)  
Thanks for your solution @Sreejith.

Harini said: (Dec 8, 2016)  
How could n (S) be 36?

Yallaling Dashavant said: (Jan 7, 2017)  
Sum 9 means (1,8)(2,7)(3,6)(4,5)(5,4)(6 3)(7,2).

Means 8/36 = 2/9.

Sarita said: (Jan 27, 2017)  
How can it be 6x6?

Two throws of a dice mean 6+6. Your answer can only be till 12, not 36.

Neetu Sanghvi said: (Feb 24, 2017)  
I agree @Sree Tulasi.

Prince said: (Jul 21, 2017)  
Why we take these cases only?

(3+6) = 9.
(4+5) = 9.
(5+4) = 9.
(6+3) = 9.

Pooja Gm said: (Apr 7, 2018)  
Why we take this case only?
(3+6)
(4+5)
(5+4)
(6+3).

This also possible;
(7+2),
(1+8),
(2+7),
(8+1),

Please explain the reason.

Swathi said: (May 11, 2018)  
Why we should not use the permutations here?like sum 9 can appear in either (6, 3) or (3, 6) , (5, 4) or (4, 5). Why we only choose the one possibility?

Joshua said: (Feb 7, 2019)  
Because in a throw of two dices there is only 6x6, is the last the number won't Or should not exceed 6.

Arif said: (Feb 15, 2019)  
At first you draw sample space then you find pair which sum is 9, (1,1), (1,2),....... (5,4), (6,3),(3,6), (4,5).

Total pair 36 and sum of 9 pair is 4 them p(sum 9)= 4 ÷ 36 = 1/9.

Rrk said: (Feb 22, 2019)  
Is throwing a dice two times and throwing two dice together, same?

Please, anyone, clear me.

Surya said: (Jul 4, 2019)  
One dice have six faces so here we have two dices, so the formula is n2 (n Square). So 6*6 =36.

Nikolay said: (Aug 1, 2019)  
@Pooja Gm.

Dice does not have 8 surfaces it has only 6.

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